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Speaker:

Jeroen Sijsling
Affiliation:

Utrecht U/MPI
Date:

Wed, 2011-02-09 14:15 - 15:15
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar A (1;e)-curve is a quotient of the upper half plane that is of genus 1 and ramifies above only one point. We explore the finite list, due to Kisao Takeuchi, of arithmetic (1;e)-curves, which are those (1;e)-curves that allow a natural finite-to-one correspondence with a Shimura curve coming from a quaternion algebra over a totally real field. After defining the notion of a canonical model of such an arithmetic (1;e)-curve, we show how to calculate these canonical models by using explicit methods such as p-adic uniformizations and Belyi maps along with modular techniques involving the Shimura congruence relation and Hilbert modular forms.

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